For decades, the defense business has been plagued by not having a reliable, deterministic method to know when the Kalman filter solution for passive ranging application is reliable for use by the fighter pilot. This has made it hard to accurately assess when the ranging solution can be used for situation awareness and weapons use. To date, ad hoc rules-of-thumb have been used to assess when the estimate of the Kalman filter standard deviation on range is thought to be reliable.
The use of passive sensor angle measurements to compute the location of surface and airborne radio frequency (RF) emitters or targets for low observable fighter aircraft is vital to ensure mission success and pilot survivability. The onboard electronic warfare sensor suite consists of multiple short baseline interferometers, SBI, that detect the radar emissions from the emitters in the battle space. The angle measurement accuracy is a function of emitter frequency, emitter angle-off-array-boresight, SBI array length, the signal-to-noise ratio, the number of RF pulses processed by the EW system, and overall array phase error. The SBI parameters consequently yield different 1-sigma values over time. Because the EW system has no control over the emitters, the measurements can arrive either synchronously or asynchronously. The sensor may also be on unmanned aerial vehicles, fast-moving surface and sub-surface vessels, or helicopters.
By way of example, a fighter aircraft flies straight-and-level with pre-planned, coordinated heading changes at waypoints in the mission. In the course of a mission, the pilot will encounter unexpected pop-up surface or airborne emitters that he needs to either avoid or respond to quickly. Pilot responses may include the use of defensive or offensive weapons, or a simple change in aircraft orientation with respect to the emitter. In both cases, the electronic warfare system processes SBI measurements. Sometimes the electronic warfare system will be able to regulate the measurement update rate, and this can assist convergence in the passive ranging solution.
Thus, for many years, in passive ranging applications the location of an emitter, be it an RF, infrared or acoustic emitter, has been determined with geolocation techniques utilized in an electronic warfare tracker in which the range and bearing to a particular emitter is ascertained. The perennial problem is that one cannot determine the reliability of the range estimate, although various methods of predicting range error have been used.
Chief in these predictive methods is the use of sigma-range derived from the updated state vector error covariance matrix associated with a Kalman filter. In general the sigma value is supposed to specify the reliability of the range measurement.
Whether it is a system using long-baseline interferometry or other systems for ascertaining angle of arrival of radiation from a target, the Kalman filter takes the noisy sensor angle measurements and in an iterative process refines or smoothes the noisy measurements and produces a derived range estimate. The result is a one-over-square-root improvement in the angle measurement error and a consequent improvement in range estimate.
However, the quality or trueness of the range estimate is unknown.
Over the many years, investigators have used an updated state vector error covariance matrix derivable from the Kalman filter to estimate the range sigma value for the range estimates produced by the filter. The Kalman filter estimates the 3-state vector and converts to range by computing the square root of the sum of the squares of the state variables.
Using the latest state vector and the updated state vector error covariance matrix, the Kalman filter generates an estimate of the quality of the range estimate in terms of the one-sigma range value.
For instance, assuming that one has a detectable target at 100 miles from a platform, and further assuming a one-sigma range uncertainty of 5 miles, then at the platform at which the geolocation sensor is located, one knows that the target is within plus or minus 5 miles around the 100-mile measured value. This gives an approximate 68% confidence level in the estimated range. If one uses a two-sigma value, then one is 95% confident of the range estimate falling between 90 and 110 miles about the range estimate.
The problem historically has been that over the years no one has come up with appropriate correction factors to multiply the value of sigma by so that range quality can be reliably ascertained. Many different rules of thumb have been tried without success.
In short, when using the Kalman filter to passively estimate range to a stationary target, there is no way of ascertaining the veracity of the tracking quality.
In the past, in order to improve the sigma range value, when a particular measurement has been made given known coordinates and parameters, one can establish a tailored multiplier or weighting scheme for the one-sigma value. However, this weighting scheme is only valid for that particular scenario. Whether or not the particular weighting scheme is applicable to other scenario circumstances is never known. Unfortunately the weighting scheme can either be optimistic, meaning that it gives a confidence level that is too high for the range measurement, or it could be much too pessimistic. One never knows whether the weighting scheme for the one-sigma range value is appropriately set by simply observing the noisy angle measurements that are processed.
One would very much like to be able to establish a confidence level that, for instance, for 95% of the time, the range measurement is within 10% of the true range, or “truth.”
In summary, even with the best weighting schemes for the one-sigma range value, this value is oftentimes too erroneous. The one-sigma range value as weighted with tailored weights is oftentimes more predictable from a theoretical viewpoint when, for instance, the platform is an aircraft flying along a straight path over a surveilled area. Given such a scenario, one can adapt the weighting scheme to make the sigma prediction correspond to reality.
On the other hand, if the aircraft is executing high G turns or has a path that is non-linear, then the so-called fudge factors that multiply the one-sigma value can, for instance, indicate that a measured range is within 10% of truth when in fact it is only within 30% of truth.
Thus in the past and historically, what investigators do is to generate a specially tailored multiplier for the sigma range value that comes out of the Kalman filter in the hope that the altered sigma metric corresponds to some sense of truth. However, in the, prior attempts at generating appropriate multipliers for sigma range values, one does not know whether one has improved the situation. It has sometimes been said that anybody's guess for sigma is as good as anyone else's.
The result is that utilizing sigma range as a way of looking at range accuracy is unreliable.
By way of further background, the way that one traditionally computes the percent range error, PRE, is simply to multiply the absolute value of the difference between the true range and the range estimate by 100, then divided by the true range. One then wants to make sure that the percent range error reduces to an acceptable region, for instance 10% or any intermediate value useful to the pilot and the onboard Mission Systems planning software. The reason that the sigma range value does not accurately indicate what the range error is, is that the sigma value could either be too pessimistic, i.e., higher than what it really should have been, or it could be too pessimistic. Either way, if one cannot trust one's range estimates to be accurate to, say, within 10%, one cannot derive a particular battlefield advantage.
It will be appreciated that passively ranging against any kind of target of interest utilizes primarily azimuth-only measurements. These azimuth-only measurements are used to compute range, with the range-sensing equipment being located, for instance, on aircraft, high-speed boats patrolling a harbor or coastal region, for instance, for homeland security, helicopters and surveillance aircraft such as E2C, Hawkeye, AWACS and UAVs or unmanned aerial vehicles. All of these platforms carry sensors that can measure angle to the different targets of interest, which can be processed to estimate range. The key question is how does one trust the range estimate out of the angle of arrival algorithms used on such platforms.
If one can establish that the range error is, for instance, 10%, one could accurately launch missiles, drop air-to-ground bombs, or in general deploy any type of countermeasure for which knowing the geolocation of the target is important. These geopositioning sensors, which utilize angle of arrival, are used not only to ascertain the geolocation of the target, but also motion as well.